Multi-part Gompertz growth problem
Growth of an individual chicken is modelled by the Gompertz differential equation . This gives the chicken's weight (in kilograms) in terms of constants and . Time is days after reaching a weight of 0.25 kilograms.
i. What aspect of the chicken growth does the term describe?
I have no idea what aspect this describes. Can anyone point me in the right direction about how to think about this sort of problem?
ii. Use separation of variables to find the general solution to this differential equation.
I think I can attempt this one. I'll give it a go and post my working. Essentially I'm finding an equation for though right?
iii. In the case that and , find the time at which the chicken weighs 4 kilograms. What meanings and units do these constants have?
Is this simply a matter of calculating t using the equation from ii and substituting in the specified variables?
iv. Does the chicken have a maximum (or asymptotic) weight, and what is it?
Think I can work this one out once I have ii and iii.
v. At what time does the value of have a maximum? This gives the maximum growth rate of the chicken.
Think I can work this one out too. Will post working.